function pi = mc_stat_distrib(P)% MC_STAT_DISTRIB Compute stationary distribution of a Markov chain% function pi = mc_stat_distrib(P)% % Each row of P should sum to one; pi is a column vector% Kevin Murphy, 16 Feb 2003% The stationary distribution pi satisfies pi P = pi% subject to sum_i pi(i) = 1,  0 <= pi(i) <= 1% Hence% (P'  0n   (pi  = (pi %  1n  0)    1)     1)% or P2 pi2 = pi2.% Naively we can solve this using (P2 - I(n+1)) pi2 = 0(n+1)% or P3 pi2 = 0(n+1), i.e., pi2 = P3 \ zeros(n+1,1)% but this is singular (because of the sum-to-one constraint).% Hence we replace the last row of P' with 1s instead of appending ones to create P2, % and similarly for pi.n = length(P);P4 = P'-eye(n);P4(end,:) = 1;pi = P4 \ [zeros(n-1,1);1];